Question

If P (A) = 0.3, P (B) = 0.6, P (B/A) = 0.5, find P (A ∪ B).

Answer 1

$$\begin{gathered} \mathrm{P}\left(\frac{B}{A}\right)=\frac{\mathrm{P}\left(A\cap B\right)}{\mathrm{P}\left(A\right)} \\ \Rightarrow 0.5=\frac{\mathrm{P}\left(A\cap B\right)}{0.3} \\ \Rightarrow \mathrm{P}\left(A\cap B\right)=0.5\times 0.3 \\ \Rightarrow \mathrm{P}\left(A\cap B\right)=0.15 \\ \text{Now,} \\ \mathrm{P}\left(A\cup B\right)=\mathrm{P}\left(A\right)+\mathrm{P}\left(B\right)-\mathrm{P}\left(A\cap B\right) \\ =0.3+0.6-0.15 \\ =0.9-0.15 \\ =0.75 \end{gathered}$$